Policy data analysis discussion ch14

Journal of the Formosan Medical Association (2011) 110, 695e700

Available online at www.sciencedirect.com

journal homepage: www.jfma-online.com

ORIGINAL ARTICLE

A multivariable logistic regression equation to evaluate prostate cancer

Jhih-Cheng Wang a, Steven K. Huan a, Jinn-Rung Kuo b, Chin-Li Lu c, Hung Lin a, Kun-Hung Shen a,*

a Division of Urology, Departments of Surgery, Chi-Mei Medical Center, Tainan, Taiwan b Division of Neurosurgery, Department of Surgery, Chi-Mei Medical Center, Tainan, Taiwan c Department of Medical Research, Chi-Mei Medical Center, Tainan, Taiwan

Received 29 January 2010; received in revised form 14 May 2010; accepted 9 August 2010

KEYWORDS Logistic regression; men’s health; probability; prostate cancer; risk factor; score

* Corresponding author. Division of U Taiwan 710.

E-mail address: tratadowang@gma

0929-6646/$ - see front matter Copyr doi:10.1016/j.jfma.2011.09.005

Background/Purpose: A possible means of decreasing prostate cancer mortality is through improved early detection. We attempted to create an equation to predict the likelihood of having prostate cancer. Methods: Between January 2005 and May 2008, patients who received prostate biopsies were retrospective evaluated. The relationship between the possibility of prostate cancer and the following variables were evaluated: age; serum prostate specific antigen (PSA) level, prostate volume, numbers of prostatic biopsies, digital rectal examination (DRE) findings, and the pres- ence of hypoechoic nodule under transrectal ultrasonography. Results: A multivariate regression model was created to predict the possibility of having pros- tate cancer, and a receiver-operating characteristic (ROC) curve was drawn based on the predictive scoring equation. Using a predictive equation, P Z 1/(1 � e�x), where X Z �4.88, þ 1.11 (if DRE positive), þ 0.75 (if hypoechoic nodule of prostate present), þ 1.27 (when 7 < PSA � 10), þ 2.02 (when 10 < PSA � 24), þ 2.28 (when 24 < PSA � 50), þ 3.93 (when 50 < PSA), þ 1.23 (when 65 < age � 75), þ 1.66 (when 75 < age), followed by ROC curve analysis, we showed that the sensitivity was 88.5% and specificity was 79.1% in predicting the possibility of prostate cancer. Conclusion: Clinicians can tailor each patient’s follow-up according to the nomogram based on this equation to increase the efficacy of evaluating for prostate cancer. Copyright ª 2011, Elsevier Taiwan LLC & Formosan Medical Association. All rights reserved.

rology, Department of Surgery, Chi-Mei Medical Center, 901 Chung Hwa Road, Yung Kang City, Tainan,

il.com (K.-H. Shen).

ight ª 2011, Elsevier Taiwan LLC & Formosan Medical Association. All rights reserved.

696 J.-C. Wang et al.

Prostate cancer is the most common solid malignancy in men, with an estimated 218,890 new cases and 27,050 deaths in 2007 in the United States.1 From a literature review, the specific cause has not yet known, but consid- erable evidence suggests that both genetics and environ- ment play a role in the origin and evolution of this disease. A possible means of decreasing the prostate cancer mortality is through improved early detection. Recent studies have shown that the measurement of serum prostate specific antigen (PSA) concentration in addition to digital rectal examination (DRE) and transrectal ultrasonography (TRUS) of the prostate enhances the early detection of prostate cancer.2,3 However, there is controversy about how these tests should be used because they have appreciable false- negative and false-positive results.4 False-negative rates remain of concern, with estimates that an office-based TRUS-guided biopsy misses about 30% of clinically signifi- cant prostate cancer.5 The aim of our study is to determine the independent predictors of prostate cancer and develop a multivariate logistic regression equation to predict its occurrence. These predicting variables include age, PSA level, prostate volume, DRE, and numbers of biopsies and hypoechoic prostate nodules.

Materials and methods

Patients who received TRUS-guided biopsies of the prostate were retrospectively evaluated and enrolled in the study from January 2005 to May 2008 in a medical center in southern Taiwan. The ethics committee of the hospital approved this study. Medical charts were reviewed and laboratory data were collected from each patient. None of the men had any of the following signs or symptoms of prostate disease: hematuria, hematospermia, dysuria, frequency, urgency, weak urine stream, or bone pain. They all underwent TRUS-biopsy of the prostate with surgical ultrasonography (Biplane transducer 8808 mode, 10 MHz, BK Medical, Herlev, Denmark). The key indications for TRUS prostate biopsy were abnormal DRE (including indurations, asymmetry, or irregularities of the prostate), hypoechoic prostate lesions on ultrasound examination, or abnormal PSA level (>4 ng/dl; Chemiluminescent Microparticle Immuno- assay, ARCHITECT System, Abbott Ireland Diagnostic Division, Sligo, Ireland). Urology surgeons performed all DREs, even among healthy individuals. Blood samples were obtained before or at least 1 week after the DRE. The data extracted from charts included the most recent serum PSA level, DRE findings, number of biopsies, and pathologies of biopsies. Pathologic information was collected from surgical reports, and clinical information, including DRE findings, prostate volume and numbers of biopsies were collected primarily from a standard form completed by the treating physician on the day of the procedure. Other clinical information, including patient age and PSA level, were obtained from all other documents available in the patients’ medical records.

The relationships between age, prostate volume, number of biopsies, PSA level, DRE findings, presence of hypoechoic prostate nodules, and pathology reports were evaluated.

Using ultrasound for TRUS-guided prostate biopsy was an office-based procedure, performed under local anesthesia

with patients in the left-lateral decubitus position. The probe was inserted transrectally and the sonograms were displayed simultaneously in the transverse and sagittal planes. Before the procedure, all men were given enemas containing phosphate and sodium biphosphate, as well as antimicrobial prophylaxis.

Biopsies were performed by urologists and the numbers of biopsies from each patient were all �10 specimens. If there were obvious hypoechoic prostate lesions on the ultrasound images, five specimens were taken from those areas, while the remaining specimens were obtained randomly from the peripheral and transitional zones of each lobe. If no hypoechoic prostate lesion was observed on TRUS imaging, all specimens were randomly obtained from the peripheral and transitional zones of each lobe equally.

Data were expressed as means � standard deviations (SD) or count (percentage), as appropriate. Student’s t test was for continuous variables and a chi-square test was completed for categorical variables to compare the difference between two groups. The forward stepwise procedure was performed to construct a multiple logistic regression model, equating the relationships between clinical characteristics and occurrence of prostate cancer. A nonsignificant result (p Z 0.152) of Hosmer and Leme- show test supported the goodness-of-fit of our model. According to the equation, clinicians may rapidly calculate each patient’s score (logit value) and used the nomogram to yield a predicted probability of prostate cancer. Moreover, we used the likelihood to plot receiver operating charac- teristic (ROC) curve and found out an optimal cut-off point of predicted probability by maximizing the Youden Index. Sensitivity and specificity of this cut point was assessed. All data were analyzed using a qualified statistical software package (SPSS for Windows, Version 16.0, SPSS Inc., Chi- cago, Illinois, USA). A p of less than 0.05 was considered significant.

Results

Among the 356 men suspected of having prostate cancer, the mean age was 66.9 � 9.9 years (range, 35e89 years). Prostate cancer occurred in 87 men (24.4%). The mean age of these 87 patients was 72.2 � 8.0 years (range, 54e86 years). A total of 323 men (90.7%) had serum PSA concen- trations of greater than 4.0 ng/ml, 131 (36.7%) had abnormal findings on DRE, and 130 (36.5%) had hypoechoic prostate nodules on TRUS imaging. We found that 119 (33.4%) had PSA >4 ng/ml with abnormal DRE findings, 109 (30.6%) had PSA >4 ng/ml with hypoechoic prostate nodules on TRUS imaging, and 71 (19.9%) had abnormal DRE findings with hypoechoic prostate nodules on TRUS imaging. A total of 62 (17.4%) patients met all of the three inclusion criteria. Patients and their clinical characteristics are summarized in Table 1.

Patients with prostate cancer were older and more likely to have a higher PSA level than the noncancer group (Table 2, both p < 0.001). Positive findings in DRE and hypoechoic prostate nodules were also significantly higher in the cancer group. (Table 2, p < 0.001, p Z 0.005, respectively).

Multivariate logistic regression was performed on the significant variables extracted from the previous step to

Table 1 Detecting rate of prostate cancer in various combinations.

Variables Cancer p

Total count, % No. count, % Yes count, %

DRE � 224 (63.1) 198 (73.9) 26 (29.9) <0.001 þ 131 (36.9) 70 (26.1) 61 (70.1)

Hypoechoic nodule � 226 (63.5) 191 (71.0) 35 (40.2) <0.001 þ 130 (36.5) 78 (29.0) 52 (59.8)

PSA (ng/ml) �4 33 33 (12.3) 0 (0) <0.001 >4 323 (90.7) 236 (87.7) 87 (100)

PSA >4 and DRE (þ) No 236 (66.5) 210 (78.4) 26 (29.9) <0.001 Yes 119 (33.5) 58 (21.6) 61 (70.1)

PSA >4 and hypoechoic nodule (þ) No 247 (69.4) 212 (78.8) 35 (40.2) <0.001 Yes 109 (30.6) 57 (21.2) 52 (59.8)

DRE (þ) and hypoechoic nodule (þ) No 284 (80.0) 239 (89.2) 45 (51.7) <0.001 Yes 71 (20.0) 29 (10.8) 42 (48.3)

PSA >4 and DRE (þ) and hypoechoic nodule (þ) No 293 (82.5) 248 (92.5) 45 (51.7) <0.001 Yes 62 (17.5) 20 (7.5) 42 (58.3)

DRE Z digital rectal examination; PSA Z prostate specific antigen.

Prostate cancer evaluating equation 697

determine the independent association of each variable with prostate cancer. Thus, the final model contained four variables: age, five PSA levels, DRE, and hypoechoic pros- tate nodules. The results showed AGE2 (65 < age � 75; odds ratio [OR] Z 3.43, confidence interval [CI] Z 1.44e8.19, p Z 0.006), AGE3 (75 < age; OR Z 5.27, CI Z 2.13e13.05, p < 0.001), DRE (OR Z 3.05, CI Z 1.57e5.92, p Z 0.001), hypoechoic prostate nodules (OR Z 2.11, CI Z 1.10e4.07, p Z 0.026), PSA2 (7 < PSA � 10; OR Z 3.57, CI Z 1.07e 11.95, p Z 0.039), PSA3 (10 < PSA � 24; OR Z 7.51, CI Z 2.65e21.30, p < 0.001), PSA4 (24 < PSA � 50; OR Z 9.76, CI Z 2.71e35.12, p < 0.001), and PSA5 (50 < PSA; OR Z 50.94, CI Z 15.43e168.12, p < 0.001) were

Table 2 Association between clinical characteristics and prosta

Variables

No (n Z 269)

Age (y)a 66.9 � 9.9 Biopsy no.a 12.0 � 2.4 Prostate volume (ml)a 48.4 � 38.3 DREb � 198 (88)

þ 70 (53) Hypoechoic noduleb � 191 (85)

þ 78 (60) PSA (ng/ml)a 59.7 � 174.8 PSA stratificationb �2.50 22 (100)

2.51e4.00 11 (100) 4.01e10.00 141 (92) >10.01 95 (56)

Digits in cells represent mean � SD or count (percentage). a Data were compared by Student’s t test. b Data were compared by chi-square test.

independently associated with prostate cancer (Table 3). No matter PSA level and age are continuous factors or stratified factors; they are independent factor in evalu- ating prostate cancer (Tables 2 and 3). We put PSA level and age as stratified factors into the predictive model of prostate cancer because of no evidence showed PSA level or age has linear relationship with prostate cancer. And the stratification of PSA level and age are according to the method of making minimal statistic bias in numbers.

The predicted probability (P) of having prostate cancer was estimated by the multiple logistic regression model: P Z 1/(1�e�x), where X Z �4.88 þ 1.11 (if DRE positive) þ 0.75 (if hypoechoic nodule present) þ 1.27 (when 7 < PSA

te cancer.

Cancer p

Yes (n Z 87) Total (n Z 356)

67.7 � 9.8 72.2 � 8.0 <0.001 12.1 � 2.3 11.7 � 2.9 0.260 49.8 � 41.7 44.3 � 24.8 0.137 26 (12) 224 (100) <0.001 61 (47) 131 (100)

35 (16) 226 (100) <0.001 52 (40) 130 (100)

20.7 � 67.4 180.3 � 304.2 <0.001 0 (0) 22 (100) <0.001 0 (0) 11 (100) 13 (8) 154 (100) 74 (44) 169 (100)

Table 3 Multivariate logistic regression model to predict the risk of prostate cancer.

Variables B OR (eB) 95% CI of OR p

DRE No Ref. Ref. Yes 1.11 3.05 1.57e5.92 0.001

Hypoechoic nodule

No Ref. Ref. Yes 0.75 2.11 1.10e4.07 0.026

PSA (ng/ml)

�7 Ref. Ref. >7e10 1.27 3.57 1.07e11.95 0.039 >10e24 2.02 7.51 2.65e21.30 <0.001 >24e50 2.28 9.76 2.71e35.12 <0.001 >50 3.93 50.94 15.43e168.12 <0.001

Age �65 Ref. Ref. >65e75 1.23 3.43 1.44e8.19 0.006 >75 1.66 5.27 2.13e13.05 <0.001

Intercept �4.88 0.01 <0.001 B Z regression coefficient; OR Z odds ratio in favor of having prostate cancer; Ref Z referent group. Figure 2 Receiver-operating characteristic curve. Points

(black arrow) on the receiver-operating characteristic curve represent the possibility levels generated from the logistic regression analysis that was used to select the optimal cut point. A predicted probability of 0.23 provided a sensitivity of 88.5% and a specificity of 79.1%.

698 J.-C. Wang et al.

� 10) þ 2.02 (when 10 < PSA � 24) þ 2.28 (when 24 < PSA � 50) þ 3.93 (when 50 < PSA) þ 1.23 (when 65 < age � 75) þ 1.66 (when 75 < age). This is also shown as Fig. 1. The predictors of the model were selected by a stepwise proce- dure. Using a ROC curve analysis based on the prognostic model score, a cut point for prediction of prostate cancer (P) was defined as a value �0.23. The sensitivity of the equation was 88.5%, while the specificity was 79.1% for predicting the possibility of prostate cancer [area under the curve Z 0.89, 95% CI Z 0.85e0.93 (Fig. 2)]. And the ROC curve of these four combined factors is better than the ROC curve of each of these four factors (data not showed here).

Discussion

DRE has always been the primary method for evaluating the prostate. However, Smith and Catalona6 showed that the DRE was investigator-dependent and had great interexaminer

Figure 1 An equation predicting likelihood of prostate cancer.

variability. Jacobsen and others7 reported that one of the effects of DRE screening for prostate cancer was that men screened with DRE were less likely to die from prostate cancer, and screening could have prevented 50%e70% of prostate cancer deaths. However, both Friedman et al8 and Chodak et al9 showed little or no additional beneficial effect for DRE in a screening program. In our study, the univariate analysis showed that DRE had a relationship with prostate cancer (p < 0.001). With multiple logistic regression modeling, the adjusted OR for predicting prostate cancer was significant for DRE (OR Z 3.05, CI Z 1.57e5.92, p Z 0.001). Our results revealed DRE is an independent predictor of prostate cancer, which is consistent with former reports.

TRUS is widely available for most physicians and has become the most commonly used imaging modality for the prostate.10 It detects cancers as hypoechoic lesions, but finding a hypoechoic lesion is not specific for prostate cancer because benign processes, such as prostatitis or infarction,10 also appear as hypoechoic lesions. In Dyke’s11

study, the group consisted of 164 consecutive men with a solitary hypoechoic prostatic nodule visible at TRUS, and carcinoma was diagnosed on the basis of biopsy directed at the suspicious hypoechoic nodule alone in 56 patients (79%).11 In our study, the results of a univariate analysis showed that the hypoechoic prostate nodule had a rela- tionship with prostate cancer (p < 0.001). In the multiple logistic regression analysis, the adjusted OR for predicting prostate cancer was significant for hypoechoic nodules (OR Z 3.05, CI Z 1.10e4.07, p Z 0.026). Our results showed that the presence of a hypoechoic prostate nodule is an independent predictor for prostate cancer.

PSA is a protein that is produced by the prostatic epithelium. It is sufficiently specific for the prostate gland in clinical practice. Although PSA is organ-specific, it is not

Figure 3 (A) An example of a patient’s clinical data; (B) a rapid scoring system using a logistic regression model; (C) a nomogram for calculating the predicted probability of prostate cancer.

Prostate cancer evaluating equation 699

cancer-specific. Benign disease of the prostate can also cause serum PSA to rise.12 Furthermore, PSA values can be influenced by prostate manipulation, e.g., DRE, TRUS, or cystoscopy, and, to a variable degree, acute prostatitis and urinary retention can also affect the PSA value.13 Rarely happened prostate infarction can also affect PSA level greatly.14 In the study by Chris et al,13 who evaluated the screening tests for detection of prostate cancer of 1726 men, total serum PSA was the most important single predictor of prostate cancer, followed by DRE. In our study, to minimize statistical bias, we separated patients into five different categories of PSA levels (Table 3); they were all related to prostate cancer, but they had different contri- butions to prostate-cancer likelihood. The higher the PSA level, the greater the contribution was.

The factors that determine the risk of developing pros- tate cancer are not well known; however, some have been identified. Age is the most obvious risk factor with the incidence of the disease increasing with age. About 75% of patients with prostate cancer are diagnosed after 65 years of age.14 A 75-year-old man has an average life expectancy of another 10 years, so very few men aged 75 years or older would experience a mortality benefit. Regardless of whether or not age was treated as a continuous or cate- gorical variable, it always had a statistically significant relationship with the prostate cancer. Thus, we divided age into three groups: Group 1 (age �65 years), Group 2 (65 < age � 75 years), and Group 3 (age >75 years). Group 1 served as the baseline for comparison. The contribution of age as a risk factor for prostate cancer as shown in Table 3.

We combined ROC curve analysis and the multivariate logistic regression equation to evaluate the predictive accuracy of the four variables for predicting the possibility

of prostate cancer. All four of the variables, which have been previously shown to be related to prostate cancer, had good accuracy for predicting the possibility of prostate cancer, with sensitivity of 88.5% and specificity of 79.1%. Since these four variables in the scoring model were clini- cally simple to attain, we considered that the derived equation was clinically useful to predict the possibility of prostate cancer in daily practice.

At our hospital, clinicians do not need to remember the equation because we programmed it into Microsoft Excel (Microsoft Corporation, USA) on the outpatient department computer. When clinicians suspect prostate cancer, they input the patient’s PSA level, age, DRE findings (1 if positive finding and 0 for negative) and the presence or absence of a hypoechoic prostate nodule (1 for present and 0 for not) into the established input data column (Fig. 3A). The computer will then calculate the final total score (Fig. 3B). Finally, they examine Fig. 3C to get the estimated likeli- hood of prostate cancer for the patient. Clinicians can tell patients the possibility of having prostate cancer according to these four easily obtained variables and can tailor each patient’s follow-up treatment accordingly. Therefore, patients may become more willing to undergo TRUS-guided biopsy to increase the efficacy of screening for prostate cancer.

Our analysis has limitations. It is a retrospective study and the prostate cancer risk equation developed has not yet been validated. Despite these limitations, our equation is based on the variables obtained from patients within the same race and in a local environment; thus, we believe it will be useful in the design of further studies because genetics and the environment play roles in the initial disease and its evolution.

700 J.-C. Wang et al.

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